<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="seq_1.html#NM1">Real_Sequence</a>;<br/>



<b>assume </b><a NAME="E1:56"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 2</span>)</span>
 ;<br/>

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="nat_1.html#NM1">Nat</a>] means <span class="p1">(<span class="default"><a href="series_3.html#K1" target="_self">Partial_Product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">a<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>;<br/>
<span class="p1">(<span class="default"><a href="series_3.html#K1" target="_self">Partial_Product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> 0 = 
<font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> 0
<b>by </b><i><a class="ref" href="series_3.html#D1" target="_self">Def1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 0</span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> 0</span>)</span> <a href="binop_2.html#K23">+</a> 2</span>)</span>
<b>by </b><i><a class="txt" href="series_3.html#E1:56"><i><font color="Green">E30</font></i></a></i>
<br/>.= 
1 <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> 0</span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="square_1.html#T85">SQUARE_1:85</a></i>
;<br/>
<a NAME="E3:56"/><b>then </b><i><font color="Green">E31</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[0]
 
;<br/>
<a NAME="E4:56"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] holds <br/><font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font> <a href="binop_2.html#K23">+</a> 1]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><a NAME="E1:56_2"/><i><font color="Green">E33</font></i>: 
<span class="p1">(<span class="default"><a href="series_3.html#K1" target="_self">Partial_Product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:56_2"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_3.html#K1" target="_self">Partial_Product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="binop_2.html#K12">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K12">/</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="binop_2.html#K12">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="series_3.html#E1:56_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<a NAME="E3:56_2"/><b>then </b><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_3.html#K1" target="_self">Partial_Product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="binop_2.html#K12">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">1 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T77">XCMPLX_1:77</a></i>;<br/>
<a NAME="E4:56_2"/><i><font color="Green">E35</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> 0
 
<b>by </b><i><a class="ref" href="xreal_1.html#T129">XREAL_1:129</a></i>;<br/>
<a NAME="E5:56_2"/><i><font color="Green">E36</font></i>: 
(  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp;  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 )
 
<b>by </b><i><a class="ref" href="square_1.html#T93">SQUARE_1:93</a></i>;<br/>
<a NAME="E6:56_2"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="series_3.html#E5:56_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="xreal_1.html#T131">XREAL_1:131</a></i>;<br/>
<a NAME="E7:56_2"/>
111 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 112 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/>
<a NAME="E8:56_2"/><b>then </b>
<span class="p1">(<span class="default">111 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">112 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 64
 
<b>by </b><i><a class="ref" href="xreal_1.html#T9">XREAL_1:9</a></i>;<br/>
<a NAME="E9:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">111 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 63</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K11">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">112 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 64</span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8">XREAL_1:8</a></i>;<br/>
<a NAME="E10:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default">36 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">27 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">28 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">84 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default">48 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 64
 
;<br/>
<a NAME="E11:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default">36 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">27 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">28 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">84 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default">48 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 64
 
;<br/>
<a NAME="E12:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default">36 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">27 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">28 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">84 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default">48 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 64
 
;<br/>
<a NAME="E13:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 2</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default">36 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">27 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">28 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">84 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default">48 <a href="binop_2.html#K24">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 64
 
<b>by </b><i><a class="ref" href="newton.html#T13">NEWTON:13</a></i>;<br/>
<a NAME="E14:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default">4 <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 2</span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> 3</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">36 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">27 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">28 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">84 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 64
 
;<br/>
<a NAME="E15:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default">4 <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 2</span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> 3</span>)</span> <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">36 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">27 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">28 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">84 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 64
 
<b>by </b><i><a class="ref" href="newton.html#T10">NEWTON:10</a></i>;<br/>
<a NAME="E16:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default">4 <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> 3</span>)</span> <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">36 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">27 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">28 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">84 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> <span class="p1">(<span class="default">2 <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 64
 
<b>by </b><i><a class="txt" href="series_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E17:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default">4 <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> 3</span>)</span> <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">36 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">27 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">28 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">84 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 2</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 64
 
<b>by </b><i><a class="ref" href="newton.html#T13">NEWTON:13</a></i>;<br/>
<a NAME="E18:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default">4 <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> 3</span>)</span> <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">36 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">27 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">28 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">84 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="prepower.html#K3">|^</a> 1</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 64
 
<b>by </b><i><a class="txt" href="series_3.html#E1"><i><font color="Green">Lemma1</font></i></a></i>;<br/>
<a NAME="E19:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><span class="p1">(<span class="default">4 <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> 3</span>)</span> <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">36 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">27 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">28 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">84 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 63 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default">12 <a href="binop_2.html#K11">*</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p4">(<span class="default">48 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">64 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 64
 
<b>by </b><i><a class="ref" href="newton.html#T10">NEWTON:10</a></i>;<br/>
<a NAME="E20:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">12 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 9</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 16</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span>
 
;<br/>
<a NAME="E21:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p3">(<span class="default">12 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> 9</span>)</span> <a href="binop_2.html#K24">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">4 <a href="binop_2.html#K11">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default">16 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> 16</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span>
 
;<br/>
<a NAME="E22:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default">4 <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span>
 
;<br/>
<a NAME="E23:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default">4 <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span>
 
;<br/>
<a NAME="E24:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">3 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> <span class="p2">(<span class="default">4 <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span>
 
;<br/>
<a NAME="E25:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">3 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">4 <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span>
 
;<br/>
<a NAME="E26:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">3 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">4 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span>
 
;<br/>
<a NAME="E27:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K9">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p5">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="binop_2.html#K24">*</a> 4</span>)</span></span>)</span> <a href="binop_2.html#K9">+</a> <span class="p2">(<span class="default">4 <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span>
 
;<br/>
<a NAME="E28:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span>
 
;<br/>
<a NAME="E29:56_2"/><b>then </b>
 <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="series_3.html#E4:56_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="square_1.html#T94">SQUARE_1:94</a></i>;<br/>
<a NAME="E30:56_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="square_1.html#K7">sqrt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span> <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="square_1.html#T97">SQUARE_1:97</a></i>;<br/>
<a NAME="E31:56_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="square_1.html#T97">SQUARE_1:97</a></i>;<br/>
<a NAME="E32:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span> <a href="square_1.html#K5">^2</a> </span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="square_1.html#T89">SQUARE_1:89</a></i>;<br/>
<a NAME="E33:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span></span>)</span> <a href="binop_2.html#K11">*</a> 1
 
<b>by </b><i><a class="ref" href="square_1.html#T89">SQUARE_1:89</a></i>;<br/>
<a NAME="E34:56_2"/><b>then </b>
<span class="p1">(<span class="default">1 <a href="binop_2.html#K24">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 3</span>)</span></span>)</span> <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span> <a href="binop_2.html#K11">*</a> <span class="p2">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 7</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="series_3.html#E5:56_2"><i><font color="Green">E36</font></i></a>, <a class="txt" href="series_3.html#E6:56_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="xreal_1.html#T104">XREAL_1:104</a></i>;<br/>
<a NAME="E35:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_3.html#K1" target="_self">Partial_Product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> 1</span>)</span> <a href="binop_2.html#K12">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="series_3.html#E3:56_2"><i><font color="Green">E34</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E36:56_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="series_3.html#K1" target="_self">Partial_Product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="binop_2.html#K11">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="seq_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K23">+</a> 1</span>)</span></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="series_3.html#E1:56"><i><font color="Green">E30</font></i></a></i>;<br/>
<b>hence </b><a NAME="E37:56_2"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>3</sub></font> <a href="binop_2.html#K23">+</a> 1]
 <b>by </b><i><a class="ref" href="series_3.html#D1" target="_self">Def1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E5:56"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>]
 
<b>from </b><i><a class="ref" href="nat_1.html#S1">NAT_1:sch 1</a>(<a class="txt" href="series_3.html#E3:56"><i><font color="Green">E31</font></i></a>, <a class="txt" href="series_3.html#E4:56"><i><font color="Green">E32</font></i></a>);<br/></i>
<b>hence </b><a NAME="E6:56"/>
<span class="p1">(<span class="default"><a href="series_3.html#K1" target="_self">Partial_Product</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="binop_2.html#K12">/</a> <span class="p1">(<span class="default"><a href="square_1.html#K7">sqrt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default">3 <a href="binop_2.html#K24">*</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_2.html#K23">+</a> 4</span>)</span></span>)</span>
 ;<br/>


</div>
